Research On Variable Weight Combination Forecast Of Compositional Data Based On Genetic Algorithm

The compositional data is a kind of multi-dimensional data with special spatial structure,which is usually used to study the proportion of each part in the whole.Therefore,the compositional data reflects the relative information between data rather than the data itself.However,the premise of general statistical analysis method is the normality hypothesis,and the fixed sum limitation of the compositional data often makes this data has multicollinearity and doesn't satisfy the hypothesis premise,so the commonly used statistical methods are not suitable for the prediction and analysis of such data.For this reason,Aitchison proposed a logratio transformation method to avoid the limitation of constants' sum,that is,the method maps compositional data space to Euclidean space,so that the classical statistical methods can continue to be applied to the statistical analysis of compositional data.Initially,the attention to the compositional data is mainly used to study the proportion of various chemical components in the rock,and then it is gradually promoted to analyze the development trend of regional industrial structure,and predict the household living expenses of urban and rural residents,etc.And it has become an important type of statistical analysis data in the fields of economy,society,science and technology.Accordingly,the prediction of compositional data provides a theoretical basis for experts' decisions and suggestions to a certain extent.Combination forecasting method is one of the hot topics in current forecasting field.And it minimizes the influence of uncertainties in single forecasting model,that is,it combines the single forecasting values of different models in the form of different weights to improve the reliability and stability of forecasting results.However,in the existing literature,the variable weight combination forecasting method is seldom used in the prediction of compositional data.Therefore,it is necessary to predict and analyze the compositional data in the form of combination.The main con-tents of this paper are as follows:(1)The variable weight combination forecasting method based on additive logratio transformation is applied to the compositional data related to time change.In this method,the weight coefficients of the single prediction model at different times are different,so the variable weight has better adaptability for the prediction data.(2)In view of the single objective function of most combination forecasting,the variable weight combination forecasting is optimized to minimize the sum of absolute relative errors.However,the form of the optimization function is complex and non-differentiable,and the general method of obtaining weights can't achieve the desired effect.Therefore,this paper uses genetic algorithm without basic mathematical constraints to obtain the sample option weights,and it uses the average method to determine the prediction option coefficients,so as to reduce the prediction error and make the prediction results more comprehensively,systematically and have better adaptability.